The dollar value $v(t)$ of a certain car model that is $t$ years old is given by the following exponential function.
\[
v(t)=18,500(0.92)^{t}
\]
Find the initial value of the car and the value after 13 years.
Round your answers to the nearest dollar as necessary.
EXPLANATION
Answer
Final Answer: The initial value of the car is \(\boxed{18500}\) and the value after 13 years is \(\boxed{6258}\).
Step 1 ：The dollar value $v(t)$ of a certain car model that is $t$ years old is given by the following exponential function: \[v(t)=18,500(0.92)^{t}\]
Step 2 ：The initial value of the car is when $t=0$. We can substitute $t=0$ into the function to find the initial value: \[v(0)=18,500(0.92)^{0} = 18500\]
Step 3 ：The value of the car after 13 years is found by substituting $t=13$ into the function: \[v(13)=18,500(0.92)^{13} = 6258\]
Step 4 ：Final Answer: The initial value of the car is \(\boxed{18500}\) and the value after 13 years is \(\boxed{6258}\).
